%I #7 Mar 31 2012 14:02:21
%S 0,1,2,3,4,7,6,11,8,5,14,25,12,19,22,9,16,47,10,31,28,29,50,13,24,21,
%T 38,15,44,61,18,137,128,43,94,49,20,55,62,53,56,97,58,115,100,27,26,
%U 37,48,69,42,113,76,73,30,79,88,33,122,319,36,41,274,39,64,121,86,185
%N Doubly-recursed cross-domain bijection from N to GF(2)[X]. Variant of A091204 and A106444.
%C Differs from A091204 for the first time at n=32, where A091204(32)=32, while a(32)=128. Differs from A106444 for the first time at n=11, where A106444(11)=13, while a(11)=25.
%H A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(0)=0, a(1)=1, a(p_i) = A014580(a(i)) for primes p_i with index i and for composites n = p_i^e_i * p_j^e_j * p_k^e_k * ..., a(n) = A048723(a(p_i), a(e_i)) X A048723(a(p_j), a(e_j)) X A048723(a(p_k), a(e_k)) X ..., where X stands for carryless multiplication of GF(2)[X] polynomials (A048720) and A048723(n, y) raises the n-th GF(2)[X] polynomial to the y:th power.
%e a(5) = 7, as 5 is the 3rd prime, a(3)=3 and the third irreducible GF(2)[X] polynomial x^2+x+1 is encoded as A014580(3) = 7. a(11) = 25, as 11 is the 5th prime, a(5)=7 and the seventh irreducible GF(2)[X] polynomial x^4+x^3+1 is encoded as A014580(7) = 25. a(32) = a(2^5) = A048723(a(2),a(5)) = A048723(2,7) = 128.
%Y Inverse: A106447. Variant: A091204.
%K nonn
%O 0,3
%A _Antti Karttunen_, May 09 2005